This isn't BvS where WB was rebooting so a new Batman just 4 years after Bale was warranted.
Let me preface this by saying I think I'm one of 4 or 5 consistently, serious X-Men movie fans. . .BUT, you're right. Instead, this is FoX-Men, where we get a "soft" reboot of sorts with almost every new entry in the franchise!
A new Wolverine would make no sense at all in this franchise because Jackman existed in both the past and future time periods. And again, no actor will wanna try to live up to that.
After 9 films covering his origin, Weapon X, his time in Japan, his time with the X-Men and his last ride in Logan, they've pretty much exhausted the character anyway.
All that's left to do with him in this franchise is have Jackman finally don the cowl for a legendary guest appearance in DP2.
The next 7 years of X-Men frankly don't need Wolverine as a star anymore. There's dozens of mutants left to flesh out, starting with Cable.
I think plenty of actors would be thrilled to have the opportunity to star as one of the top 5 comic book super heroes in existence, irrespective of what Jackman did. As for exhausting his character, having read his comics and been a fan since I was at least 5 years old, I can't agree with you on that. Plenty of uncharted space, and plenty of opportunities to improve on missteps we've seen thus far (including the lackluster Japanese excursion and lame origin story). We haven't seen a galactic story like the comic version of Dark Phoenix or the Brood, we haven't seen a lot of Wolvie the Canadian agent or mercenary, we haven't seen Alpha Flight, we haven't seen the Savage Land, we haven't seen Genosha, we haven't seen Mojo, we haven't seen Proteus, we haven't seen Arcade, we haven't seen Excalibur, etc. Lots of options for Wolvie to show up and provide some entertainment.
It just wouldn't sit well with me at all. He's the one character and actor who bridged the original cast and the 'new' cast. Changing Wolverine would be a mind**** too far even for the Fox-verse IMO. Plus, a new actor in the role will want to put his own stamp on it - and if its supposed to be the same Logan that Jackman played he shouldn't really do that, he should be sticking close to Jackman's portrayal.
I take the other approach--it is better to go your own route and forget as much as you can about Jackman's effort. In a sense, that shows more respect to Jackman, because you acknowledge that he mastered it. Think about Routh Superman. . .probably not the best approach. And this is in line with what I said before, that I think the character would be better served taking a secondary role in the films, and providing color to the ensemble, rather than being the de facto leader and focus each time out. But I would be supportive of any Wolvie moving forward.
As for the recast being jarring, it probably would be for some. But to me, life is about change! I love what Jackman did for us, but the character--like Spider-Man or Batman--is bigger than his take on it. Let's mix it up, recast him with a different take, give him the suit, make him edgier than Jackman typically was, force him to make tough decisions in a morally gray environment when the rest of the team can't or won't, etc.